Consumer groups have urged all rail operators to follow Virgin Trains' decision to offer compensation in the form of a cheque as the default option rather than travel vouchers.
The policy will apply on Virgin's east and west coast routes.
Anthony Smith, chief executive at the independent watchdog Transport Focus, said: "Passengers will be pleased to see Virgin Trains offering cash compensation as the first option. This is a positive step forward and we want to see more operators follow suit."
He added that many people are not claiming the compensation they are entitled to.
Richard Lloyd, executive director of consumer group Which?, claimed passengers are "rightly frustrated by the significant barriers" to obtaining compensation.
"It is good to see Virgin Trains setting the pace by offering cash as the default option for compensation," he said.
"We would urge all train operating companies to act quickly to implement this, and further changes, to improve the process for their customers."
A spokesman for the Rail Delivery Group, representing Network Rail and train operators, said: "Many train companies are already offering their customers cash as compensation for delays as default, whether in the form of a cheque or voucher to be cashed at a ticket office.
"Operators are continuing to look at other ways to make it even simpler and quicker for people to get their delay compensation in cash."
New arrangements came into effect in July last year meaning all rail passengers can request to receive their payout in cash.
In October Virgin Trains launched a system whereby west coast travellers who buy Advance tickets through its website receive money directly on to their payment cards if they are entitled to compensation.
Some 5% of services run by Virgin Trains were either cancelled, at least 30 minutes late, or missed a scheduled stop in the 12 months to March 5, according to Network Rail figures.
The average for rail firms across England and Wales is 3%.
Graham Leech, group commercial director at Virgin Trains, said: "We're committed to making claiming compensation simpler and clearer for customers.
"We never want passengers to suffer delays or disruption but when things do go wrong we want to put it right."